John R. Silvester

Determinants of Block Matrices

Let us first consider the 2 x 2 matrices and Their sum and product are given by Here the entries a, b, c, d, e, f, g, h can come from a field, such as the real numbers, or more generally from a ring, commutative or not.

Droz-Farny constructions

Notation: If A, B are points, then AB denotes the line AB rather than just the segment from A to B , unless stated otherwise. If l, m are lines, then their meet is denoted l m . The circle through points A, B and C (the circumcircle of Δ ABC ) is denoted ⊙ ABC . Given Δ ABC , let the points X i , Y i , Z i , lie on BC, CA, AB , respectively, for i = 1, 2, 3; that is, three distinct points on each side of the triangle, and suppose